Prince Rupert's cube

In geometry, Prince Rupert's cube (named after Prince Rupert of the Rhine) is the largest cube that can pass through a hole cut through a unit cube, i.e. through a cube whose sides have length 1, without splitting the cube into two pieces. Its side length is approximately 6% larger than that of the unit cube through which it passes. The problem of finding the largest square that lies entirely within a unit cube is closely related, and has the same solution.If two points are placed on two adjacent edges of a unit cube, each at a distance of 3/4 from the point where the two edges meet, then the distance between the two points will bePrince Rupert's cube is named after Prince Rupert of the Rhine. According to a story recounted in 1693 by English mathematician John Wallis, Prince Rupert wagered that a hole could be cut through a cube, large enough to let another cube of the same size pass through it. Wallis showed that in fact such a hole was possible (with some errors that were not corrected until much later), and Prince Rupert won his wager.The construction of a physical model of Prince Rupert's cube is made challenging by the accuracy with which such a model needs to be measured, and the thinness of the connections between the remaining parts of the unit cube after the hole is cut through it. For the maximally sized-inner cube with length 1.06... relative to the length 1 outer cube, constructing a model has been called 'mathematically possible but practically impossible'.The cube is not the only regular body that can pass through a hole cut into a copy of itself; the same is true for the regular tetrahedron and octahedron.